Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 470 · 40 questions

How to solve it (Divide by 7 first): Circle: circumference = 2 × π × r; area = π × r × r. With π = 22/7, divide the radius by 7 first. Cube of edge a: volume = a × a × a, surface area = 6 × a × a. Cuboid: volume = l × b × h, surface area = 2 × (lb + bh + hl). Make every length k times as long: areas become k × k times as big, volumes k × k × k times.

1. 1.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 1232 sq cm
2. 2.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 27 times (c) 3 times (d) 9 times
3. 3.A cuboid is 10 cm long, 5 cm wide and 5 cm high. What is its volume? (a) 251 cu cm (b) 20 cu cm (c) 250 cu cm (d) 50 cu cm
4. 4.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 4 times (c) 8 times (d) 5 times
5. 5.A cube has edges of 9 cm. What is its volume? (a) 324 cu cm (b) 729 cu cm (c) 486 cu cm (d) 27 cu cm
6. 6.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 6 times (c) 27 times (d) 9 times
7. 7.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
8. 8.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 8 times (c) 4 times (d) 16 times
9. 9.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
10. 10.A cube has edges of 5 cm. What is its total surface area? (a) 125 sq cm (b) 25 sq cm (c) 150 sq cm (d) 100 sq cm
11. 11.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
12. 12.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 440 cm (d) 220 cm
13. 13.A cube has edges of 10 cm. What is its total surface area? (a) 600 sq cm (b) 100 sq cm (c) 400 sq cm (d) 1000 sq cm
14. 14.A cube has edges of 9 cm. What is its total surface area? (a) 81 sq cm (b) 729 sq cm (c) 324 sq cm (d) 486 sq cm
15. 15.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 22 cm (d) 88 cm
16. 16.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 4 times (c) 64 times (d) 16 times
17. 17.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 88 cm (d) 352 cm
18. 18.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm
19. 19.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 66 cm (d) 264 cm
20. 20.A cuboid is 11 cm long, 8 cm wide and 7 cm high. What is its total surface area? (a) 442 sq cm (b) 221 sq cm (c) 616 sq cm (d) 884 sq cm
21. 21.A cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 18 cu cm (c) 144 cu cm (d) 216 cu cm
22. 22.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 2 times (c) 5 times (d) 8 times
23. 23.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
24. 24.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 27 times (c) 6 times (d) 3 times
25. 25.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 8 cu cm (c) 6 cu cm (d) 16 cu cm
26. 26.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 25 times (c) 125 times (d) 5 times
27. 27.A cuboid is 10 cm long, 8 cm wide and 5 cm high. What is its volume? (a) 80 cu cm (b) 23 cu cm (c) 340 cu cm (d) 400 cu cm
28. 28.A cuboid is 7 cm long, 6 cm wide and 8 cm high. What is its volume? (a) 21 cu cm (b) 42 cu cm (c) 336 cu cm (d) 292 cu cm
29. 29.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 5544 sq cm
30. 30.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 16 times (b) 64 times (c) 8 times (d) 4 times
31. 31.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 352 cm (d) 2464 cm
32. 32.A cube has edges of 10 cm. What is its volume? (a) 1000 cu cm (b) 30 cu cm (c) 600 cu cm (d) 400 cu cm
33. 33.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
34. 34.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 8 times (b) 2 times (c) 4 times (d) 6 times
35. 35.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 12 sq cm (b) 64 sq cm (c) 16 sq cm (d) 32 sq cm
36. 36.A cuboid is 10 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 164 cu cm (b) 120 cu cm (c) 40 cu cm (d) 17 cu cm
37. 37.A cuboid is 10 cm long, 2 cm wide and 9 cm high. What is its volume? (a) 21 cu cm (b) 256 cu cm (c) 180 cu cm (d) 20 cu cm
38. 38.A cuboid is 5 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 9 cu cm (b) 48 cu cm (c) 10 cu cm (d) 20 cu cm
39. 39.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
40. 40.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 110 cm (d) 3850 cm

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